################################################################################
################################################################################
## 1.1 Pontos de mudança e IC95% ###############################################
################################################################################
################################################################################
################################################################################
## 1.1.1 Ponto de mudança e IC95% Glicose ______________________________________
################################################################################
LS_IC95_Ponto_inflexao_glicose<-11.72
Ponto_inflexao_glicose<-10.90
LI_IC95_Ponto_inflexao_glicose<-10.09
################################################################################
## 1.1.2 Ponto de mudança e IC95% HOMA-IR ______________________________________
################################################################################
LS_IC95_Ponto_inflexao_HOMA_IR<-12.87
Ponto_inflexao_HOMA_IR<-11.23
LI_IC95_Ponto_inflexao_HOMA_IR<-9.58
################################################################################
## 1.1.3 Ponto de mudança e IC95% Colesterol Total _____________________________
################################################################################
LS_IC95_Ponto_inflexao_CT<-17.89
Ponto_inflexao_CT<-15.85
LI_IC95_Ponto_inflexao_CT<-13.81
################################################################################
## 1.1.4 Ponto de mudança e IC95% HDL-c ________________________________________
################################################################################
LS_IC95_Ponto_inflexao_HDL.c<-17.98
Ponto_inflexao_HDL.c<-16.11
LI_IC95_Ponto_inflexao_HDL.c<-14.23
################################################################################
## 1.1.5 Ponto de mudança e IC95% LDL-c ________________________________________
################################################################################
LS_IC95_Ponto_inflexao_LDL.c<-18.73
Ponto_inflexao_LDL.c<-16.61
LI_IC95_Ponto_inflexao_LDL.c<-14.49
################################################################################
## 1.1.6 Ponto de mudança e IC95% Triglicérides ________________________________
################################################################################
LS_IC95_Ponto_inflexao_TRI<-14.35
Ponto_inflexao_TRI<-13.08
LI_IC95_Ponto_inflexao_TRI<-11.82
################################################################################
################################################################################
## 1.2 Instalação Pacote R #####################################################
################################################################################
################################################################################
Pacotes_R <- c("rmarkdown","knitr","multimode","modeest","rstatix","univOutl",
"readxl","utf8","pwr","forecast","MultNonParam","ggplot2","earth",
"plotly","DT","kableExtra","dplyr","stats","segmented","caret",
"refineR","SciViews","rcompanion","effectsize","car","moments",
"ggpubr","writexl","metafor","gridExtra","grid","meta")
if(sum(as.numeric(!Pacotes_R %in% installed.packages())) != 0){
instalador <- Pacotes_R[!Pacotes_R %in% installed.packages()]
for(i in 1:length(instalador)) {
install.packages(instalador, dependencies = TRUE)
break()}
sapply(Pacotes_R, require, character = TRUE)
} else {
sapply(Pacotes_R, require, character = TRUE)
}
## rmarkdown knitr multimode modeest rstatix univOutl
## TRUE TRUE TRUE TRUE TRUE TRUE
## readxl utf8 pwr forecast MultNonParam ggplot2
## TRUE TRUE TRUE TRUE TRUE TRUE
## earth plotly DT kableExtra dplyr stats
## TRUE TRUE TRUE TRUE TRUE TRUE
## segmented caret refineR SciViews rcompanion effectsize
## TRUE TRUE TRUE TRUE TRUE TRUE
## car moments ggpubr writexl metafor gridExtra
## TRUE TRUE TRUE TRUE TRUE TRUE
## grid meta
## TRUE TRUE
library(utf8)
options(es.use_symbols = TRUE)
options(scipen = 999)
library(ggplot2)
library(dplyr)
set.seed(200707042) # Para resultados reproduzíveis
################################################################################
################################################################################
## 1.3 Gráfico Sobreposição dos IC95% ##########################################
################################################################################
################################################################################
# Criar um dataframe com os dados
exames <- c("Colesterol total",
"HDL-c",
"LDL-c",
"Triglicérides",
"HOMA-IR",
"Glicose")
ponto_corte <- c(Ponto_inflexao_CT,
Ponto_inflexao_HDL.c,
Ponto_inflexao_LDL.c,
Ponto_inflexao_TRI,
Ponto_inflexao_HOMA_IR,
Ponto_inflexao_glicose)
inferior <- c(LI_IC95_Ponto_inflexao_CT,
LI_IC95_Ponto_inflexao_HDL.c,
LI_IC95_Ponto_inflexao_LDL.c,
LI_IC95_Ponto_inflexao_TRI,
LI_IC95_Ponto_inflexao_HOMA_IR,
LI_IC95_Ponto_inflexao_glicose)
superior <- c(LS_IC95_Ponto_inflexao_CT,
LS_IC95_Ponto_inflexao_HDL.c,
LS_IC95_Ponto_inflexao_LDL.c,
LS_IC95_Ponto_inflexao_TRI,
LS_IC95_Ponto_inflexao_HOMA_IR,
LS_IC95_Ponto_inflexao_glicose)
df <- data.frame(exames, ponto_corte, inferior, superior)
# Calcular os intervalos de confiança de 83%
df$inferior_95 <- df$ponto_corte - (df$superior - df$ponto_corte) * sqrt(.95/.95)
df$superior_95 <- df$ponto_corte + (df$superior - df$ponto_corte) * sqrt(.95/.95)
# Verificar se os intervalos de confiança se sobrepõem
df <- df %>%
arrange(inferior_95, superior_95) %>%
mutate(sobreposicao = c(FALSE, inferior_95[-1] <= superior_95[-n()]))
# Atribuir cores aos intervalos de confiança com base na sobreposição
df$cor <- with(df, cumsum(!sobreposicao))
# Organizando o conjunto de dados
df <- df[order(-df$ponto_corte),]
# Criando o gráfico
graf_IC95<-ggplot(df, aes(x = factor(exames, levels = df$exames),
y = ponto_corte, color = factor(cor))) +
geom_linerange(aes(ymin = inferior_95, ymax = superior_95), size = 0.8) +
geom_point(size = 2) +
geom_errorbar(aes(ymin = inferior_95, ymax = superior_95), width = 0.2, size = 0.5) +
coord_flip() +
scale_color_manual(values = c("black", rainbow(length(unique(df$cor)) - 1)),
name = "Sobreposição") +
labs(x = "Exames", y = "Pontos de inflexão da Prolactina (ng/mL)", title = "") +
scale_y_continuous(breaks = seq(min(df$inferior_95), max(df$superior_95), by = 0.5)) +
theme_bw() +
theme(
axis.text.x = element_text(size = 14, color = "black", angle = 45, hjust = 1),
axis.text.y = element_text(size = 14, color = "black"),
axis.line = element_line(colour = "black"),
axis.title = element_text(size = 16),
legend.position = "none",
panel.grid.minor = element_blank()
)
## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
graf_IC95
graf_IC95_2<-ggplotly(graf_IC95)
graf_IC95_2
ggsave("2_Figuras/Fig._IC95%_Sobrepostos.png",
plot = graf_IC95, device = "png")
################################################################################
################################################################################
## 1.4 Estimação do alfa para a comparações de IC95% ###########################
################################################################################
################################################################################
################################################################################
### 1.4.1 Glicose vs HOMA-IR ___________________________________________________
################################################################################
#### 1.4.1.1 Calcular a probabilidade P (Formula 3) ____________________________
################################################################################
calc_prob <- function(rho, gamma) {
2 * pnorm(-1.96 * (1 + rho) / sqrt(1 - 2 * gamma * rho + rho^2))
}
#### 1.4.1.2 Calcular a probabilidade P no caso específico γ=0 e ρ=1 (Formula 4)
################################################################################
calc_prob_spec <- function() {
2 * pnorm(-1.96 * 2 / sqrt(2))
}
#### 1.4.1.3 Calcular o nível de confiança (Formula 6) _________________________
################################################################################
conf_level <- function(z) {
(1 - 2 * pnorm(-z)) * 100
}
#### 1.4.1.4 Calcular a probabilidade P com um valor de z ajustado (Formula 7) _
################################################################################
calc_prob_z <- function(rho, gamma, z) {
2 * pnorm(-z * (1 + rho) / sqrt(1 - 2 * gamma * rho + rho^2))
}
#### 1.4.1.5 Calcular valor de z para uma probabilidade P de 5% (Formula 10) ___
################################################################################
calc_z <- function(rho, gamma, p) {
q <- 1 - (p/ 2)
z <- abs(qnorm(1 - q))
z * sqrt(1 - 2 * gamma * rho + rho^2) / (1 + rho)
}
#### 1.4.1.6 Calcular o nível de confiança correspondente (Formula 11) _________
################################################################################
calc_conf_level <- function(rho, gamma, z) {
(1 - 2 * pnorm(-z * sqrt(1 - 2 * gamma * rho + rho^2) / (1 + rho))) * 100
}
#### 1.4.1.7 Ratio σ_2/σ_1 _____________________________________________________
################################################################################
rho <- 2.02
#### 1.4.1.8 Coeficiente de Correlação entre os Pontos de inflexão _____________
################################################################################
gamma <- 0
#### 1.4.1.9 Resultados ________________________________________________________
################################################################################
print(paste("Probabilidade P:", calc_prob(rho, gamma)))
## [1] "Probabilidade P: 0.00863651414535271"
print(paste("Probabilidade P (caso específico):", calc_prob_spec()))
## [1] "Probabilidade P (caso específico): 0.00557372453517213"
print(paste("Nível de confiança para z=1.3859:", conf_level(1.386)))
## [1] "Nível de confiança para z=1.3859: 83.4253096509899"
print(paste("Nível de confiança para z=1.96:", conf_level(1.96)))
## [1] "Nível de confiança para z=1.96: 95.0004209703559"
print(paste("Probabilidade P para z=1.3859:", calc_prob_z(rho,gamma,z= 1.386)))
## [1] "Probabilidade P para z=1.3859: 0.0633054870466338"
print(paste("Probabilidade P para z=1.96:", calc_prob_z(rho,gamma, z= 1.96)))
## [1] "Probabilidade P para z=1.96: 0.00863651414535271"
print(paste("Valor de z para obter P=5%:", calc_z(rho, gamma, p = 0.05)))
## [1] "Valor de z para obter P=5%: 1.4628173466919"
print(paste("Valor de z para obter P=0.5%:", calc_z(rho, gamma, p = 0.0056)))
## [1] "Valor de z para obter P=0.5%: 2.06763122431127"
print(paste("Nível de confiança correspondente:",
round(calc_conf_level(rho, gamma, 1.96),1)))
## [1] "Nível de confiança correspondente: 85.6"
print(paste("Nível de confiança correspondente:",
round(calc_conf_level(rho, gamma, 2.77),1)))
## [1] "Nível de confiança correspondente: 96.1"
################################################################################
### 1.4.2 HOMA-IR vs Triglicérides _____________________________________________
################################################################################
#### 1.4.2.1 Calcular a probabilidade P (Formula 3) ____________________________
################################################################################
calc_prob <- function(rho, gamma) {
2 * pnorm(-1.96 * (1 + rho) / sqrt(1 - 2 * gamma * rho + rho^2))
}
#### 1.4.2.2 Calcular a probabilidade P no caso específico γ=0 e ρ=1 (Formula 4)
################################################################################
calc_prob_spec <- function() {
2 * pnorm(-1.96 * 2 / sqrt(2))
}
#### 1.4.2.3 Calcular o nível de confiança (Formula 6) _________________________
################################################################################
conf_level <- function(z) {
(1 - 2 * pnorm(-z)) * 100
}
#### 1.4.2.4 Calcular a probabilidade P com um valor de z ajustado (Formula 7) _
################################################################################
calc_prob_z <- function(rho, gamma, z) {
2 * pnorm(-z * (1 + rho) / sqrt(1 - 2 * gamma * rho + rho^2))
}
#### 1.4.2.5 Calcular valor de z para uma probabilidade P de 5% (Formula 10) ___
################################################################################
calc_z <- function(rho, gamma, p) {
q <- 1 - (p/ 2)
z <- abs(qnorm(1 - q))
z * sqrt(1 - 2 * gamma * rho + rho^2) / (1 + rho)
}
#### 1.4.2.6 Calcular o nível de confiança correspondente (Formula 11) _________
################################################################################
calc_conf_level <- function(rho, gamma, z) {
(1 - 2 * pnorm(-z * sqrt(1 - 2 * gamma * rho + rho^2) / (1 + rho))) * 100
}
#### 1.4.2.7 Ratio σ_2/σ_1 _____________________________________________________
################################################################################
rho <- 0.77
#### 1.4.2.8 Coeficiente de Correlação entre os Pontos de inflexão _____________
################################################################################
gamma <- 0
#### 1.4.2.9 Resultados ________________________________________________________
################################################################################
print(paste("Probabilidade P:", calc_prob(rho, gamma)))
## [1] "Probabilidade P: 0.00598231806075919"
print(paste("Probabilidade P (caso específico):", calc_prob_spec()))
## [1] "Probabilidade P (caso específico): 0.00557372453517213"
print(paste("Nível de confiança para z=1.3859:", conf_level(1.386)))
## [1] "Nível de confiança para z=1.3859: 83.4253096509899"
print(paste("Nível de confiança para z=1.96:", conf_level(1.96)))
## [1] "Nível de confiança para z=1.96: 95.0004209703559"
print(paste("Probabilidade P para z=1.3859:", calc_prob_z(rho,gamma,z= 1.386)))
## [1] "Probabilidade P para z=1.3859: 0.0519246155220898"
print(paste("Probabilidade P para z=1.96:", calc_prob_z(rho,gamma, z= 1.96)))
## [1] "Probabilidade P para z=1.96: 0.00598231806075919"
print(paste("Valor de z para obter P=5%:", calc_z(rho, gamma, p = 0.05)))
## [1] "Valor de z para obter P=5%: 1.39755555503473"
print(paste("Valor de z para obter P=0.5%:", calc_z(rho, gamma, p = 0.0056)))
## [1] "Valor de z para obter P=0.5%: 1.97538640749253"
print(paste("Nível de confiança correspondente:",
round(calc_conf_level(rho, gamma, 1.96),1)))
## [1] "Nível de confiança correspondente: 83.8"
print(paste("Nível de confiança correspondente:",
round(calc_conf_level(rho, gamma, 2.77),1)))
## [1] "Nível de confiança correspondente: 95.2"
################################################################################
### 1.4.3 Triglicérides vs Colesterol total ____________________________________
################################################################################
#### 1.4.3.1 Calcular a probabilidade P (Formula 3) ____________________________
################################################################################
calc_prob <- function(rho, gamma) {
2 * pnorm(-1.96 * (1 + rho) / sqrt(1 - 2 * gamma * rho + rho^2))
}
#### 1.4.3.2 Calcular a probabilidade P no caso específico γ=0 e ρ=1 (Formula 4)
################################################################################
calc_prob_spec <- function() {
2 * pnorm(-1.96 * 2 / sqrt(2))
}
#### 1.4.3.3 Calcular o nível de confiança (Formula 6) _________________________
################################################################################
conf_level <- function(z) {
(1 - 2 * pnorm(-z)) * 100
}
#### 1.4.3.4 Calcular a probabilidade P com um valor de z ajustado (Formula 7) _
################################################################################
calc_prob_z <- function(rho, gamma, z) {
2 * pnorm(-z * (1 + rho) / sqrt(1 - 2 * gamma * rho + rho^2))
}
#### 1.4.3.5 Calcular valor de z para uma probabilidade P de 5% (Formula 10) ___
################################################################################
calc_z <- function(rho, gamma, p) {
q <- 1 - (p/ 2)
z <- abs(qnorm(1 - q))
z * sqrt(1 - 2 * gamma * rho + rho^2) / (1 + rho)
}
#### 1.4.3.6 Calcular o nível de confiança correspondente (Formula 11) _________
################################################################################
calc_conf_level <- function(rho, gamma, z) {
(1 - 2 * pnorm(-z * sqrt(1 - 2 * gamma * rho + rho^2) / (1 + rho))) * 100
}
#### 1.4.3.7 Ratio σ_2/σ_1 _____________________________________________________
################################################################################
rho <- 1.61
#### 1.4.3.8 Coeficiente de Correlação entre os Pontos de inflexão _____________
################################################################################
gamma <- 0
#### 1.4.3.9 Resultados ________________________________________________________
################################################################################
print(paste("Probabilidade P:", calc_prob(rho, gamma)))
## [1] "Probabilidade P: 0.00695228737443857"
print(paste("Probabilidade P (caso específico):", calc_prob_spec()))
## [1] "Probabilidade P (caso específico): 0.00557372453517213"
print(paste("Nível de confiança para z=1.3859:", conf_level(1.386)))
## [1] "Nível de confiança para z=1.3859: 83.4253096509899"
print(paste("Nível de confiança para z=1.96:", conf_level(1.96)))
## [1] "Nível de confiança para z=1.96: 95.0004209703559"
print(paste("Probabilidade P para z=1.3859:", calc_prob_z(rho,gamma,z= 1.386)))
## [1] "Probabilidade P para z=1.3859: 0.056305423836829"
print(paste("Probabilidade P para z=1.96:", calc_prob_z(rho,gamma, z= 1.96)))
## [1] "Probabilidade P para z=1.96: 0.00695228737443857"
print(paste("Valor de z para obter P=5%:", calc_z(rho, gamma, p = 0.05)))
## [1] "Valor de z para obter P=5%: 1.42325196764921"
print(paste("Valor de z para obter P=0.5%:", calc_z(rho, gamma, p = 0.0056)))
## [1] "Valor de z para obter P=0.5%: 2.01170721350064"
print(paste("Nível de confiança correspondente:",
round(calc_conf_level(rho, gamma, 1.96),1)))
## [1] "Nível de confiança correspondente: 84.5"
print(paste("Nível de confiança correspondente:",
round(calc_conf_level(rho, gamma, 2.77),1)))
## [1] "Nível de confiança correspondente: 95.6"
################################################################################
### 1.4.4 Colesterol total vs HDL-c ____________________________________________
################################################################################
#### 1.4.4.1 Calcular a probabilidade P (Formula 3) ____________________________
################################################################################
calc_prob <- function(rho, gamma) {
2 * pnorm(-1.96 * (1 + rho) / sqrt(1 - 2 * gamma * rho + rho^2))
}
#### 1.4.4.2 Calcular a probabilidade P no caso específico γ=0 e ρ=1 (Formula 4)
################################################################################
calc_prob_spec <- function() {
2 * pnorm(-1.96 * 2 / sqrt(2))
}
#### 1.4.4.3 Calcular o nível de confiança (Formula 6) _________________________
################################################################################
conf_level <- function(z) {
(1 - 2 * pnorm(-z)) * 100
}
#### 1.4.4.4 Calcular a probabilidade P com um valor de z ajustado (Formula 7) _
################################################################################
calc_prob_z <- function(rho, gamma, z) {
2 * pnorm(-z * (1 + rho) / sqrt(1 - 2 * gamma * rho + rho^2))
}
#### 1.4.4.5 Calcular valor de z para uma probabilidade P de 5% (Formula 10) ___
################################################################################
calc_z <- function(rho, gamma, p) {
q <- 1 - (p/ 2)
z <- abs(qnorm(1 - q))
z * sqrt(1 - 2 * gamma * rho + rho^2) / (1 + rho)
}
#### 1.4.4.6 Calcular o nível de confiança correspondente (Formula 11) _________
################################################################################
calc_conf_level <- function(rho, gamma, z) {
(1 - 2 * pnorm(-z * sqrt(1 - 2 * gamma * rho + rho^2) / (1 + rho))) * 100
}
#### 1.4.4.7 Ratio σ_2/σ_1 _____________________________________________________
################################################################################
rho <- 0.92
#### 1.4.4.8 Coeficiente de Correlação entre os Pontos de inflexão _____________
################################################################################
gamma <- 0
#### 1.4.4.9 Resultados ________________________________________________________
################################################################################
print(paste("Probabilidade P:", calc_prob(rho, gamma)))
## [1] "Probabilidade P: 0.0056150059605543"
print(paste("Probabilidade P (caso específico):", calc_prob_spec()))
## [1] "Probabilidade P (caso específico): 0.00557372453517213"
print(paste("Nível de confiança para z=1.3859:", conf_level(1.386)))
## [1] "Nível de confiança para z=1.3859: 83.4253096509899"
print(paste("Nível de confiança para z=1.96:", conf_level(1.96)))
## [1] "Nível de confiança para z=1.96: 95.0004209703559"
print(paste("Probabilidade P para z=1.3859:", calc_prob_z(rho,gamma,z= 1.386)))
## [1] "Probabilidade P para z=1.3859: 0.0501830087154771"
print(paste("Probabilidade P para z=1.96:", calc_prob_z(rho,gamma, z= 1.96)))
## [1] "Probabilidade P para z=1.96: 0.0056150059605543"
print(paste("Valor de z para obter P=5%:", calc_z(rho, gamma, p = 0.05)))
## [1] "Valor de z para obter P=5%: 1.3871063441632"
print(paste("Valor de z para obter P=0.5%:", calc_z(rho, gamma, p = 0.0056)))
## [1] "Valor de z para obter P=0.5%: 1.96061688434171"
print(paste("Nível de confiança correspondente:",
round(calc_conf_level(rho, gamma, 1.96),1)))
## [1] "Nível de confiança correspondente: 83.5"
print(paste("Nível de confiança correspondente:",
round(calc_conf_level(rho, gamma, 2.77),1)))
## [1] "Nível de confiança correspondente: 95"
################################################################################
### 1.4.5 Colesterol total vs LDL-c ____________________________________________
################################################################################
#### 1.4.5.1 Calcular a probabilidade P (Formula 3) ____________________________
################################################################################
calc_prob <- function(rho, gamma) {
2 * pnorm(-1.96 * (1 + rho) / sqrt(1 - 2 * gamma * rho + rho^2))
}
#### 1.4.5.2 Calcular a probabilidade P no caso específico γ=0 e ρ=1 (Formula 4)
################################################################################
calc_prob_spec <- function() {
2 * pnorm(-1.96 * 2 / sqrt(2))
}
#### 1.4.5.3 Calcular o nível de confiança (Formula 6) _________________________
################################################################################
conf_level <- function(z) {
(1 - 2 * pnorm(-z)) * 100
}
#### 1.4.5.4 Calcular a probabilidade P com um valor de z ajustado (Formula 7) _
################################################################################
calc_prob_z <- function(rho, gamma, z) {
2 * pnorm(-z * (1 + rho) / sqrt(1 - 2 * gamma * rho + rho^2))
}
#### 1.4.5.5 Calcular valor de z para uma probabilidade P de 5% (Formula 10) ___
################################################################################
calc_z <- function(rho, gamma, p) {
q <- 1 - (p/ 2)
z <- abs(qnorm(1 - q))
z * sqrt(1 - 2 * gamma * rho + rho^2) / (1 + rho)
}
#### 1.4.5.6 Calcular o nível de confiança correspondente (Formula 11) _________
################################################################################
calc_conf_level <- function(rho, gamma, z) {
(1 - 2 * pnorm(-z * sqrt(1 - 2 * gamma * rho + rho^2) / (1 + rho))) * 100
}
#### 1.4.5.7 Ratio σ_2/σ_1 _____________________________________________________
################################################################################
rho <- 1.04
#### 1.4.5.8 Coeficiente de Correlação entre os Pontos de inflexão _____________
################################################################################
gamma <- 0
#### 1.4.5.9 Resultados ________________________________________________________
################################################################################
print(paste("Probabilidade P:", calc_prob(rho, gamma)))
## [1] "Probabilidade P: 0.00558285200782896"
print(paste("Probabilidade P (caso específico):", calc_prob_spec()))
## [1] "Probabilidade P (caso específico): 0.00557372453517213"
print(paste("Nível de confiança para z=1.3859:", conf_level(1.386)))
## [1] "Nível de confiança para z=1.3859: 83.4253096509899"
print(paste("Nível de confiança para z=1.96:", conf_level(1.96)))
## [1] "Nível de confiança para z=1.96: 95.0004209703559"
print(paste("Probabilidade P para z=1.3859:", calc_prob_z(rho,gamma,z= 1.386)))
## [1] "Probabilidade P para z=1.3859: 0.0500281392710848"
print(paste("Probabilidade P para z=1.96:", calc_prob_z(rho,gamma, z= 1.96)))
## [1] "Probabilidade P para z=1.96: 0.00558285200782896"
print(paste("Valor de z para obter P=5%:", calc_z(rho, gamma, p = 0.05)))
## [1] "Valor de z para obter P=5%: 1.38617021624533"
print(paste("Valor de z para obter P=0.5%:", calc_z(rho, gamma, p = 0.0056)))
## [1] "Valor de z para obter P=0.5%: 1.95929370662762"
print(paste("Nível de confiança correspondente:",
round(calc_conf_level(rho, gamma, 1.96),1)))
## [1] "Nível de confiança correspondente: 83.4"
print(paste("Nível de confiança correspondente:",
round(calc_conf_level(rho, gamma, 2.77),1)))
## [1] "Nível de confiança correspondente: 95"
################################################################################
### 1.4.6 HDL-c vs LDL-c _______________________________________________________
################################################################################
#### 1.4.6.1 Calcular a probabilidade P (Formula 3) ____________________________
################################################################################
calc_prob <- function(rho, gamma) {
2 * pnorm(-1.96 * (1 + rho) / sqrt(1 - 2 * gamma * rho + rho^2))
}
#### 1.4.6.2 Calcular a probabilidade P no caso específico γ=0 e ρ=1 (Formula 4)
################################################################################
calc_prob_spec <- function() {
2 * pnorm(-1.96 * 2 / sqrt(2))
}
#### 1.4.6.3 Calcular o nível de confiança (Formula 6) _________________________
################################################################################
conf_level <- function(z) {
(1 - 2 * pnorm(-z)) * 100
}
#### 1.4.6.4 Calcular a probabilidade P com um valor de z ajustado (Formula 7) _
################################################################################
calc_prob_z <- function(rho, gamma, z) {
2 * pnorm(-z * (1 + rho) / sqrt(1 - 2 * gamma * rho + rho^2))
}
#### 1.4.6.5 Calcular valor de z para uma probabilidade P de 5% (Formula 10) ___
################################################################################
calc_z <- function(rho, gamma, p) {
q <- 1 - (p/ 2)
z <- abs(qnorm(1 - q))
z * sqrt(1 - 2 * gamma * rho + rho^2) / (1 + rho)
}
#### 1.4.6.6 Calcular o nível de confiança correspondente (Formula 11) _________
################################################################################
calc_conf_level <- function(rho, gamma, z) {
(1 - 2 * pnorm(-z * sqrt(1 - 2 * gamma * rho + rho^2) / (1 + rho))) * 100
}
#### 1.4.6.7 Ratio σ_2/σ_1 _____________________________________________________
################################################################################
rho <- 1.13
#### 1.4.6.8 Coeficiente de Correlação entre os Pontos de inflexão _____________
################################################################################
gamma <- 0
#### 1.4.6.9 Resultados ________________________________________________________
################################################################################
print(paste("Probabilidade P:", calc_prob(rho, gamma)))
## [1] "Probabilidade P: 0.00566250393123794"
print(paste("Probabilidade P (caso específico):", calc_prob_spec()))
## [1] "Probabilidade P (caso específico): 0.00557372453517213"
print(paste("Nível de confiança para z=1.3859:", conf_level(1.386)))
## [1] "Nível de confiança para z=1.3859: 83.4253096509899"
print(paste("Nível de confiança para z=1.96:", conf_level(1.96)))
## [1] "Nível de confiança para z=1.96: 95.0004209703559"
print(paste("Probabilidade P para z=1.3859:", calc_prob_z(rho,gamma,z= 1.386)))
## [1] "Probabilidade P para z=1.3859: 0.0504110526112334"
print(paste("Probabilidade P para z=1.96:", calc_prob_z(rho,gamma, z= 1.96)))
## [1] "Probabilidade P para z=1.96: 0.00566250393123794"
print(paste("Valor de z para obter P=5%:", calc_z(rho, gamma, p = 0.05)))
## [1] "Valor de z para obter P=5%: 1.38848267814549"
print(paste("Valor de z para obter P=0.5%:", calc_z(rho, gamma, p = 0.0056)))
## [1] "Valor de z para obter P=0.5%: 1.96256227494246"
print(paste("Nível de confiança correspondente:",
round(calc_conf_level(rho, gamma, 1.96),1)))
## [1] "Nível de confiança correspondente: 83.5"
print(paste("Nível de confiança correspondente:",
round(calc_conf_level(rho, gamma, 2.77),1)))
## [1] "Nível de confiança correspondente: 95"
################################################################################
### 1.4.7 HDL-c vs Triglicérides _______________________________________________
################################################################################
#### 1.4.7.1 Calcular a probabilidade P (Formula 3) ____________________________
################################################################################
calc_prob <- function(rho, gamma) {
2 * pnorm(-1.96 * (1 + rho) / sqrt(1 - 2 * gamma * rho + rho^2))
}
#### 1.4.7.2 Calcular a probabilidade P no caso específico γ=0 e ρ=1 (Formula 4)
################################################################################
calc_prob_spec <- function() {
2 * pnorm(-1.96 * 2 / sqrt(2))
}
#### 1.4.7.3 Calcular o nível de confiança (Formula 6) _________________________
################################################################################
conf_level <- function(z) {
(1 - 2 * pnorm(-z)) * 100
}
#### 1.4.7.4 Calcular a probabilidade P com um valor de z ajustado (Formula 7) _
################################################################################
calc_prob_z <- function(rho, gamma, z) {
2 * pnorm(-z * (1 + rho) / sqrt(1 - 2 * gamma * rho + rho^2))
}
#### 1.4.7.5 Calcular valor de z para uma probabilidade P de 5% (Formula 10) ___
################################################################################
calc_z <- function(rho, gamma, p) {
q <- 1 - (p/ 2)
z <- abs(qnorm(1 - q))
z * sqrt(1 - 2 * gamma * rho + rho^2) / (1 + rho)
}
#### 1.4.7.6 Calcular o nível de confiança correspondente (Formula 11) _________
################################################################################
calc_conf_level <- function(rho, gamma, z) {
(1 - 2 * pnorm(-z * sqrt(1 - 2 * gamma * rho + rho^2) / (1 + rho))) * 100
}
#### 1.4.7.7 Ratio σ_2/σ_1 _____________________________________________________
################################################################################
rho <- 1.48
#### 1.4.7.8 Coeficiente de Correlação entre os Pontos de inflexão _____________
################################################################################
gamma <- 0
#### 1.4.7.9 Resultados ________________________________________________________
################################################################################
print(paste("Probabilidade P:", calc_prob(rho, gamma)))
## [1] "Probabilidade P: 0.00650149192281061"
print(paste("Probabilidade P (caso específico):", calc_prob_spec()))
## [1] "Probabilidade P (caso específico): 0.00557372453517213"
print(paste("Nível de confiança para z=1.3859:", conf_level(1.386)))
## [1] "Nível de confiança para z=1.3859: 83.4253096509899"
print(paste("Nível de confiança para z=1.96:", conf_level(1.96)))
## [1] "Nível de confiança para z=1.96: 95.0004209703559"
print(paste("Probabilidade P para z=1.3859:", calc_prob_z(rho,gamma,z= 1.386)))
## [1] "Probabilidade P para z=1.3859: 0.0543061324691342"
print(paste("Probabilidade P para z=1.96:", calc_prob_z(rho,gamma, z= 1.96)))
## [1] "Probabilidade P para z=1.96: 0.00650149192281061"
print(paste("Valor de z para obter P=5%:", calc_z(rho, gamma, p = 0.05)))
## [1] "Valor de z para obter P=5%: 1.41162382128379"
print(paste("Valor de z para obter P=0.5%:", calc_z(rho, gamma, p = 0.0056)))
## [1] "Valor de z para obter P=0.5%: 1.99527131426798"
print(paste("Nível de confiança correspondente:",
round(calc_conf_level(rho, gamma, 1.96),1)))
## [1] "Nível de confiança correspondente: 84.2"
print(paste("Nível de confiança correspondente:",
round(calc_conf_level(rho, gamma, 2.77),1)))
## [1] "Nível de confiança correspondente: 95.4"